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Stochastic programming approach to optimization under uncertainty

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Abstract

In this paper we discuss computational complexity and risk averse approaches to two and multistage stochastic programming problems. We argue that two stage (say linear) stochastic programming problems can be solved with a reasonable accuracy by Monte Carlo sampling techniques while there are indications that complexity of multistage programs grows fast with increase of the number of stages. We discuss an extension of coherent risk measures to a multistage setting and, in particular, dynamic programming equations for such problems.

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  1. School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, 30332-0205, USA

    Alexander Shapiro

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  1. Alexander Shapiro
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Shapiro, A. Stochastic programming approach to optimization under uncertainty. Math. Program. 112, 183–220 (2008). https://doi.org/10.1007/s10107-006-0090-4

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